Friedrichs Extension and Min–Max Principle for Operators with a Gap

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Standard

Friedrichs Extension and Min–Max Principle for Operators with a Gap. / Schimmer, Lukas; Solovej, Jan Philip; Tokus, Sabiha.

I: Annales Henri Poincare, Bind 21, Nr. 2, 01.02.2020, s. 327-357.

Publikation: Bidrag til tidsskriftTidsskriftartikelfagfællebedømt

Harvard

Schimmer, L, Solovej, JP & Tokus, S 2020, 'Friedrichs Extension and Min–Max Principle for Operators with a Gap', Annales Henri Poincare, bind 21, nr. 2, s. 327-357. https://doi.org/10.1007/s00023-019-00855-7

APA

Schimmer, L., Solovej, J. P., & Tokus, S. (2020). Friedrichs Extension and Min–Max Principle for Operators with a Gap. Annales Henri Poincare, 21(2), 327-357. https://doi.org/10.1007/s00023-019-00855-7

Vancouver

Schimmer L, Solovej JP, Tokus S. Friedrichs Extension and Min–Max Principle for Operators with a Gap. Annales Henri Poincare. 2020 feb. 1;21(2):327-357. https://doi.org/10.1007/s00023-019-00855-7

Author

Schimmer, Lukas ; Solovej, Jan Philip ; Tokus, Sabiha. / Friedrichs Extension and Min–Max Principle for Operators with a Gap. I: Annales Henri Poincare. 2020 ; Bind 21, Nr. 2. s. 327-357.

Bibtex

@article{009ce3714fa847d59025343523f6f518,
title = "Friedrichs Extension and Min–Max Principle for Operators with a Gap",
abstract = "Semibounded symmetric operators have a distinguished self-adjoint extension, the Friedrichs extension. The eigenvalues of the Friedrichs extension are given by a variational principle that involves only the domain of the symmetric operator. Although Dirac operators describing relativistic particles are not semibounded, the Dirac operator with Coulomb potential is known to have a distinguished extension. Similarly, for Dirac-type operators on manifolds with a boundary a distinguished self-adjoint extension is characterised by the Atiyah-PatodiSinger boundary condition. In this paper, we relate these extensions to a generalisation of the Friedrichs extension to the setting of operators satisfying a gap condition. In addition, we prove, in the general setting, that the eigenvalues of this extension are also given by a variational principle that involves only the domain of the symmetric operator. We also clarify what we believe to be inaccuracies in the existing literature.",
author = "Lukas Schimmer and Solovej, {Jan Philip} and Sabiha Tokus",
year = "2020",
month = feb,
day = "1",
doi = "10.1007/s00023-019-00855-7",
language = "English",
volume = "21",
pages = "327--357",
journal = "Annales Henri Poincare",
issn = "1424-0637",
publisher = "Springer Basel AG",
number = "2",

}

RIS

TY - JOUR

T1 - Friedrichs Extension and Min–Max Principle for Operators with a Gap

AU - Schimmer, Lukas

AU - Solovej, Jan Philip

AU - Tokus, Sabiha

PY - 2020/2/1

Y1 - 2020/2/1

N2 - Semibounded symmetric operators have a distinguished self-adjoint extension, the Friedrichs extension. The eigenvalues of the Friedrichs extension are given by a variational principle that involves only the domain of the symmetric operator. Although Dirac operators describing relativistic particles are not semibounded, the Dirac operator with Coulomb potential is known to have a distinguished extension. Similarly, for Dirac-type operators on manifolds with a boundary a distinguished self-adjoint extension is characterised by the Atiyah-PatodiSinger boundary condition. In this paper, we relate these extensions to a generalisation of the Friedrichs extension to the setting of operators satisfying a gap condition. In addition, we prove, in the general setting, that the eigenvalues of this extension are also given by a variational principle that involves only the domain of the symmetric operator. We also clarify what we believe to be inaccuracies in the existing literature.

AB - Semibounded symmetric operators have a distinguished self-adjoint extension, the Friedrichs extension. The eigenvalues of the Friedrichs extension are given by a variational principle that involves only the domain of the symmetric operator. Although Dirac operators describing relativistic particles are not semibounded, the Dirac operator with Coulomb potential is known to have a distinguished extension. Similarly, for Dirac-type operators on manifolds with a boundary a distinguished self-adjoint extension is characterised by the Atiyah-PatodiSinger boundary condition. In this paper, we relate these extensions to a generalisation of the Friedrichs extension to the setting of operators satisfying a gap condition. In addition, we prove, in the general setting, that the eigenvalues of this extension are also given by a variational principle that involves only the domain of the symmetric operator. We also clarify what we believe to be inaccuracies in the existing literature.

U2 - 10.1007/s00023-019-00855-7

DO - 10.1007/s00023-019-00855-7

M3 - Journal article

VL - 21

SP - 327

EP - 357

JO - Annales Henri Poincare

JF - Annales Henri Poincare

SN - 1424-0637

IS - 2

ER -

ID: 236317096